Question

We have to choose $11$ players for cricket team from eight batsmen, six bowlers, four all rounders and two wicket keepers in the following conditions.

Number of selections when a particular batsman and particular wicket keeper don't want to play together, is

• A. $2^{18}{C}_{10}$
• B. ${}^{18}{C}_{11}{+}^{18}{C}_{10}$
• C. ${}^{19}{C}_{10}{+}^{19}{C}_{11}$
• D. None of these

Answer 1

The correct option is B ${}^{18}{C}_{11}{+}^{18}{C}_{10}$

If the particular batsman is selected, then rest of $10$ players can be selected in ${}^{18}{C}_{10}$ ways.
If particular wicketkeeper is selected, then rest of $10$ players can be selected in ${}^{18}{C}_{10}$ ways.
If both are not selected, then number of ways is ${}^{18}{C}_{11}$.
Hence, total number of ways is $2^{18}{C}_{10}{+}^{18}{C}_{11}{=}^{19}{C}_{11}{+}^{18}{C}_{10}$.